TSTP Solution File: RNG089+2 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : RNG089+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 20:41:58 EDT 2022
% Result : Theorem 0.18s 0.42s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG089+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 10:14:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 (* PROOF-FOUND *)
% 0.18/0.42 (* BEGIN-PROOF *)
% 0.18/0.42 % SZS output start Proof
% 0.18/0.42 1. (aElementOf0 (xk) (xI)) (-. (aElementOf0 (xk) (xI))) ### Axiom
% 0.18/0.42 2. (aElement0 (xz)) (-. (aElement0 (xz))) ### Axiom
% 0.18/0.42 3. (-. (aElementOf0 (sdtasdt0 (xz) (xk)) (xI))) (aElementOf0 (sdtasdt0 (xz) (xk)) (xI)) ### Axiom
% 0.18/0.42 4. ((aElement0 (xz)) => (aElementOf0 (sdtasdt0 (xz) (xk)) (xI))) (-. (aElementOf0 (sdtasdt0 (xz) (xk)) (xI))) (aElement0 (xz)) ### Imply 2 3
% 0.18/0.42 5. (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 (xk)) (xI)))) (aElement0 (xz)) (-. (aElementOf0 (sdtasdt0 (xz) (xk)) (xI))) ### All 4
% 0.18/0.42 6. ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 (xk) W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 (xk)) (xI))))) (-. (aElementOf0 (sdtasdt0 (xz) (xk)) (xI))) (aElement0 (xz)) ### And 5
% 0.18/0.42 7. ((aElementOf0 (xk) (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 (xk) W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 (xk)) (xI)))))) (aElement0 (xz)) (-. (aElementOf0 (sdtasdt0 (xz) (xk)) (xI))) (aElementOf0 (xk) (xI)) ### Imply 1 6
% 0.18/0.42 8. (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) (aElementOf0 (xk) (xI)) (-. (aElementOf0 (sdtasdt0 (xz) (xk)) (xI))) (aElement0 (xz)) ### All 7
% 0.18/0.42 9. (aElementOf0 (xl) (xJ)) (-. (aElementOf0 (xl) (xJ))) ### Axiom
% 0.18/0.42 10. (aElement0 (xz)) (-. (aElement0 (xz))) ### Axiom
% 0.18/0.42 11. (-. (aElementOf0 (sdtasdt0 (xz) (xl)) (xJ))) (aElementOf0 (sdtasdt0 (xz) (xl)) (xJ)) ### Axiom
% 0.18/0.42 12. ((aElement0 (xz)) => (aElementOf0 (sdtasdt0 (xz) (xl)) (xJ))) (-. (aElementOf0 (sdtasdt0 (xz) (xl)) (xJ))) (aElement0 (xz)) ### Imply 10 11
% 0.18/0.42 13. (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 (xl)) (xJ)))) (aElement0 (xz)) (-. (aElementOf0 (sdtasdt0 (xz) (xl)) (xJ))) ### All 12
% 0.18/0.42 14. ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 (xl) W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 (xl)) (xJ))))) (-. (aElementOf0 (sdtasdt0 (xz) (xl)) (xJ))) (aElement0 (xz)) ### And 13
% 0.18/0.42 15. ((aElementOf0 (xl) (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 (xl) W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 (xl)) (xJ)))))) (aElement0 (xz)) (-. (aElementOf0 (sdtasdt0 (xz) (xl)) (xJ))) (aElementOf0 (xl) (xJ)) ### Imply 9 14
% 0.18/0.42 16. (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (aElementOf0 (xl) (xJ)) (-. (aElementOf0 (sdtasdt0 (xz) (xl)) (xJ))) (aElement0 (xz)) ### All 15
% 0.18/0.42 17. (-. ((aElementOf0 (sdtasdt0 (xz) (xk)) (xI)) /\ (aElementOf0 (sdtasdt0 (xz) (xl)) (xJ)))) (aElementOf0 (xl) (xJ)) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (aElement0 (xz)) (aElementOf0 (xk) (xI)) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) ### NotAnd 8 16
% 0.18/0.42 18. ((aElementOf0 (xk) (xI)) /\ ((aElementOf0 (xl) (xJ)) /\ ((xx) = (sdtpldt0 (xk) (xl))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) (aElement0 (xz)) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (-. ((aElementOf0 (sdtasdt0 (xz) (xk)) (xI)) /\ (aElementOf0 (sdtasdt0 (xz) (xl)) (xJ)))) ### ConjTree 17
% 0.18/0.42 19. ((Ex W0, (Ex W1, ((aElementOf0 W0 (xI)) /\ ((aElementOf0 W1 (xJ)) /\ ((sdtpldt0 W0 W1) = (xx)))))) /\ ((aElementOf0 (xx) (sdtpldt1 (xI) (xJ))) /\ ((Ex W0, (Ex W1, ((aElementOf0 W0 (xI)) /\ ((aElementOf0 W1 (xJ)) /\ ((sdtpldt0 W0 W1) = (xy)))))) /\ ((aElementOf0 (xy) (sdtpldt1 (xI) (xJ))) /\ (aElement0 (xz)))))) (-. ((aElementOf0 (sdtasdt0 (xz) (xk)) (xI)) /\ (aElementOf0 (sdtasdt0 (xz) (xl)) (xJ)))) (All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) (All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) ((aElementOf0 (xk) (xI)) /\ ((aElementOf0 (xl) (xJ)) /\ ((xx) = (sdtpldt0 (xk) (xl))))) ### ConjTree 18
% 0.18/0.42 20. ((aSet0 (xI)) /\ ((All W0, ((aElementOf0 W0 (xI)) => ((All W1, ((aElementOf0 W1 (xI)) => (aElementOf0 (sdtpldt0 W0 W1) (xI)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xI))))))) /\ ((aIdeal0 (xI)) /\ ((aSet0 (xJ)) /\ ((All W0, ((aElementOf0 W0 (xJ)) => ((All W1, ((aElementOf0 W1 (xJ)) => (aElementOf0 (sdtpldt0 W0 W1) (xJ)))) /\ (All W1, ((aElement0 W1) => (aElementOf0 (sdtasdt0 W1 W0) (xJ))))))) /\ (aIdeal0 (xJ))))))) ((aElementOf0 (xk) (xI)) /\ ((aElementOf0 (xl) (xJ)) /\ ((xx) = (sdtpldt0 (xk) (xl))))) (-. ((aElementOf0 (sdtasdt0 (xz) (xk)) (xI)) /\ (aElementOf0 (sdtasdt0 (xz) (xl)) (xJ)))) ((Ex W0, (Ex W1, ((aElementOf0 W0 (xI)) /\ ((aElementOf0 W1 (xJ)) /\ ((sdtpldt0 W0 W1) = (xx)))))) /\ ((aElementOf0 (xx) (sdtpldt1 (xI) (xJ))) /\ ((Ex W0, (Ex W1, ((aElementOf0 W0 (xI)) /\ ((aElementOf0 W1 (xJ)) /\ ((sdtpldt0 W0 W1) = (xy)))))) /\ ((aElementOf0 (xy) (sdtpldt1 (xI) (xJ))) /\ (aElement0 (xz)))))) ### ConjTree 19
% 0.18/0.42 % SZS output end Proof
% 0.18/0.42 (* END-PROOF *)
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